We study and provide instance-optimal algorithms in differential privacy by extending and approximating the inverse sensitivity mechanism.

An important result is that for linear functionsf it is possible to recovers from observationsx up to certain symmetries, i.e., the model isidentifiable [8].

Let t beanother F analytic in t suchthat 0 = f0 and ( t) =( ft) forallt. Intherightfigurea volumepreservingtransfor applied (see Appendix C). 3: Smoothinvariantdeformations.

In this work, we investigate the geometry of the k-th homology embedding and focus on cases reminiscent of spectral clustering. Namely, we analyze the connected sum of manifolds as a perturbation of the direct sum of their homology embeddings.